It is possible to add modifiers to a group?
Modifiers can be easily added using python.

target_lattice = bpy.data.objects['Lattice']

for obj in bpy.data.groups['Group'].objects:
    new_mod = obj.modifiers.new(type='LATTICE', name='Lattice')
    new_mod.object = target_lattice
    new_mod.strength = 0.5


Instead of all objects in a group you can use the selected objects with bpy.context.selected_objects

By changing type='LATTICE' you can add any modifier you want. Each modifier has different property names which can be seen in tooltips when python tooltips are enabled.